Here, I critically assess Larry Temkin’s book, Rethinking the Good.* [ *Based on: “Transitivity, Comparative Value, and the Methods of Ethics,” Ethics 123 (2013): 318-45. Ethics invited me to do this long review essay about the book. I accepted because, hey, publication in
The dispersing burdens example (section 1.2) is given as a supposed counterexample to transitivity, but it strikes me it has a better use.
Let’s label the decision to disperse Pi’s pain to everyone as Ai, and the decision not to disperse it as Bi. The claim is that each Ai is better than each Bi, but that the collection of all Ai from 1 to 1000 is worse than the collection of all Bi from 1 to 1000. If we accept those better-than claims, then we have a counterexample to the dominance principle (section 2.4): [A1, A2, …, A1000] and [B1, B2, …, B1000].
To avoid the counterexample, you need to argue that Ai is actually worse than Bi. Taking the count of person-days of pain as the measure of the badness gives you the desired result (1010 for Ai, 1000 for Bi), but is it a reasonable thing to do? I’d say not. The badness of 1000 consecutive days of pain is clearly worse than the badness of 1000 days spread thru (say) 80 years – about one day of pain a month. It’s possible to take one day a month off from the day-to-day without seriously impacting your life. Taking three years off is going to mess up your life. Spreading those person-days over people instead of over days has a similar benefit: no one’s life gets seriously messed up.
My error theory for thinking that the person-days of pain is a good measure of the badness is that people think that the badness can be modelled with a number. That works great for comparing badnesses (just compare the numbers), but fails horribly when it comes to measuring cumulative badness. It pumps the intuition that the badness of two or three bad things is just the sum of their individual badnesses. Our intuitions say otherwise.
The same error is seen in the argument for the repugnant conclusion (section 1.3). We are adding well-being in going from A to A+, and again going from A+ to B. The “numbers” keep going up as we move on to worlds C and D and all the way to Z. Yet Z is clearly worse than A. Supposedly the problem has to be solved by getting rid of transitivity, but it’d be better to recognize that the mapping of goodness to numbers is the problem. We have no good reason to believe that B is better than A, in spite of the good argument that the numbers must be going up.
I want to point out that I am not arguing against transitivity here. I have no reason to believe that the “betterness” that people are interested in is intransitive, in spite of the fact that we can create artificial “betterness” relations that are intransitive: rock is better than scissors which is better than paper which is better than rock. All I’m saying is that the idea that we can model betterness using Real numbers is faulty. It’s a partial order. Model it using another partial order. Maybe just assume it’s a lattice. Transitivity, check! Additivity? Not generally.
Lots of points to raise, but my response to most counter-examples to sequential transitivity is that there is something ill-posed or wrong about the endpoint (for example, what kind of intuition can we have about experiences lasting 2^99 years). I'm clearest on the case of the Repugnant Conclusion - it's wrong
The dispersing burdens example (section 1.2) is given as a supposed counterexample to transitivity, but it strikes me it has a better use.
Let’s label the decision to disperse Pi’s pain to everyone as Ai, and the decision not to disperse it as Bi. The claim is that each Ai is better than each Bi, but that the collection of all Ai from 1 to 1000 is worse than the collection of all Bi from 1 to 1000. If we accept those better-than claims, then we have a counterexample to the dominance principle (section 2.4): [A1, A2, …, A1000] and [B1, B2, …, B1000].
To avoid the counterexample, you need to argue that Ai is actually worse than Bi. Taking the count of person-days of pain as the measure of the badness gives you the desired result (1010 for Ai, 1000 for Bi), but is it a reasonable thing to do? I’d say not. The badness of 1000 consecutive days of pain is clearly worse than the badness of 1000 days spread thru (say) 80 years – about one day of pain a month. It’s possible to take one day a month off from the day-to-day without seriously impacting your life. Taking three years off is going to mess up your life. Spreading those person-days over people instead of over days has a similar benefit: no one’s life gets seriously messed up.
My error theory for thinking that the person-days of pain is a good measure of the badness is that people think that the badness can be modelled with a number. That works great for comparing badnesses (just compare the numbers), but fails horribly when it comes to measuring cumulative badness. It pumps the intuition that the badness of two or three bad things is just the sum of their individual badnesses. Our intuitions say otherwise.
The same error is seen in the argument for the repugnant conclusion (section 1.3). We are adding well-being in going from A to A+, and again going from A+ to B. The “numbers” keep going up as we move on to worlds C and D and all the way to Z. Yet Z is clearly worse than A. Supposedly the problem has to be solved by getting rid of transitivity, but it’d be better to recognize that the mapping of goodness to numbers is the problem. We have no good reason to believe that B is better than A, in spite of the good argument that the numbers must be going up.
I want to point out that I am not arguing against transitivity here. I have no reason to believe that the “betterness” that people are interested in is intransitive, in spite of the fact that we can create artificial “betterness” relations that are intransitive: rock is better than scissors which is better than paper which is better than rock. All I’m saying is that the idea that we can model betterness using Real numbers is faulty. It’s a partial order. Model it using another partial order. Maybe just assume it’s a lattice. Transitivity, check! Additivity? Not generally.
Lots of points to raise, but my response to most counter-examples to sequential transitivity is that there is something ill-posed or wrong about the endpoint (for example, what kind of intuition can we have about experiences lasting 2^99 years). I'm clearest on the case of the Repugnant Conclusion - it's wrong
https://johnquigginblog.substack.com/p/against-the-repugnant-conclusion